Fault Estimation for Discrete-Time T-S Fuzzy Systems with Unmeasurable Premise Variables Based on Fuzzy Lyapunov Functions

In this work, the fault estimation (FE) problem of discrete-time nonlinear systems subject to fault is researched by resorting to the powerful Takagi-Sugeno (T-S) fuzzy model. In contrast with the existing FE methods where the premise variables (PVs) are required to be measurable, the case of unmeasurable PVs is our primary concern. Then, a fuzzy FE observer with the estimated PVs is well-presented to achieve the reconstructions of fault and state simultaneously. Combining the introduction of a slack matrix with the application of a noncommon quadratic Lyapunov function, some stability criteria of the observer synthesis are provided against unmeasurable PVs, and completely expressed as linear matrix inequalities (LMIs). Finally, the performance of the achieved FE scheme is verified through a tunnel diode circuit.